Textbook Question
The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2. On the right, (x-y)^2 = x^2-2xy+y^2. Use special products to evaluate each expression. 102^2
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0. Review of Algebra
Polynomials Intro
1:53 minutesProblem 121
Textbook Question
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four
Verified step by step guidance1
Start by translating the English phrase into an algebraic expression. The phrase 'a number' can be represented by the variable x.
The phrase 'the sum of the number and four' means we are adding the number (x) and 4 together. This can be written as (x + 4).
The phrase 'a number decreased by' indicates subtraction. So, we subtract the sum (x + 4) from the number (x). This gives the expression x - (x + 4).
Simplify the expression x - (x + 4) by distributing the negative sign across the parentheses. This results in x - x - 4.
Combine like terms in the simplified expression. The x terms cancel out, leaving -4 as the simplified result.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this context, it represents a relationship or operation involving a variable, such as 'x'. Understanding how to translate English phrases into algebraic expressions is crucial for solving algebra problems.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept is essential for simplifying expressions correctly after they are formed.
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Simplifying Expressions
Simplifying an expression involves combining like terms and performing operations to reduce it to its simplest form. This process often includes distributing, factoring, and reducing fractions. Mastery of simplification is vital for solving equations and understanding the relationships between variables.
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